Distortion-immune position tracking using redundant measurements

ABSTRACT

A method for tracking a position of an object includes using a field sensor associated with the object to measure field strengths of magnetic fields generated by two or more field generators, wherein a measurement of at least one of the field strengths is subject to a distortion. Rotation-invariant location coordinates of the object are calculated responsively to the measured field strengths. Corrected location coordinates of the object are determined by applying to the rotation-invariant location coordinates a coordinate correcting function so as to adjust a relative contribution of each of the measured field strengths to the corrected location coordinates responsively to the distortion in the measured field strengths.

FIELD OF THE INVENTION

The present invention relates generally to magnetic position trackingsystems, and particularly to methods and systems for performing accurateposition measurements in the presence of field-distorting objects.

BACKGROUND OF THE INVENTION

Various methods and systems are known in the art for tracking thecoordinates of objects involved in medical procedures. Some of thesesystems use magnetic field measurements. For example, U.S. Pat. Nos.5,391,199 and 5,443,489, whose disclosures are incorporated herein byreference, describe systems in which the coordinates of an intrabodyprobe are determined using one or more field transducers. Such systemsare used for generating location information regarding a medical probeor catheter. A sensor, such as a coil, is placed in the probe andgenerates signals in response to externally-applied magnetic fields. Themagnetic fields are generated by magnetic field transducers, such asradiator coils, fixed to an external reference frame in known,mutually-spaced locations.

Additional methods and systems that relate to magnetic position trackingare also described, for example, in PCT Patent Publication WO 96/05768,U.S. Pat. Nos. 6,690,963, 6,239,724, 6,618,612 and 6,332,089, and U.S.Patent Application Publications 2002/0065455 A1, 2003/0120150 A1 and2004/0068178 A1, whose disclosures are all incorporated herein byreference. These publications describe methods and systems that trackthe position of intrabody objects such as cardiac catheters, orthopedicimplants and medical tools used in different medical procedures.

It is well known in the art that the presence of metallic, paramagneticor ferromagnetic objects within the magnetic field of a magneticposition tracking system often distorts the system's measurements. Thedistortion is sometimes caused by eddy currents that are induced in suchobjects by the system's magnetic field, as well as by other effects.

Various methods and systems have been described in the art forperforming position tracking in the presence of such interference. Forexample, U.S. Pat. No. 6,147,480, whose disclosure is incorporatedherein by reference, describes a method in which the signals induced inthe tracked object are first detected in the absence of any articlesthat could cause parasitic signal components. Baseline phases of thesignals are determined. When an article that generates parasiticmagnetic fields is introduced into the vicinity of the tracked object,the phase shift of the induced signals due to the parasitic componentsis detected. The measured phase shifts are used to indicate that theposition of the object may be inaccurate. The phase shifts are also usedfor analyzing the signals so as to remove at least a portion of theparasitic signal components.

SUMMARY OF THE INVENTION

Embodiments of the present invention provide improved methods andsystems for performing magnetic position tracking measurements in thepresence of metallic, paramagnetic and/or ferromagnetic objects(collectively referred to as field-distorting objects) using redundantmeasurements.

The system comprises two or more field generators that generate magneticfields in the vicinity of the tracked object. The magnetic fields aresensed by a position sensor associated with the object and converted toposition signals that are used to calculate the position (location andorientation) coordinates of the object. The system performs redundantfield strength measurements and exploits the redundant information toreduce the measurement errors caused by the presence of field-distortingobjects.

The redundant measurements comprise field strength measurements ofmagnetic fields generated by different field generators and sensed byfield sensors in the position sensor. In an exemplary embodimentdescribed herein, nine field generators and three field sensing coilsare used to obtain 27 different field strength measurements. The 27measurements are used to calculate the six location and orientationcoordinates of the tracked object, thus containing a significant amountof redundant information.

In some embodiments, a rotation-invariant coordinate correcting functionis applied to the measured field strengths to produce adistortion-corrected location coordinate of the tracked object. As willbe shown hereinbelow, the coordinate correcting function exploits theredundant location information so as to reduce the distortion level inthe corrected location coordinate.

The coordinate correcting function can be viewed as adjusting therelative contributions of the measured field strengths to the correctedlocation coordinates responsively to the respective level of thedistortion present in each of the measured field strengths. A disclosedclustering process further improves the accuracy of the coordinatecorrecting function by defining different coordinate correctingfunctions for different locations.

In some embodiments, the orientation coordinates of the tracked objectare calculated following the location calculation. Other disclosedmethods improve the accuracy of the orientation calculation in thepresence of distortion, and compensate for non-concentricity of thefield sensors of the position sensor.

In some embodiments, the redundant field strength measurements are usedto identify one or more system elements, such as field generators and/orfield sensing elements of the position sensor, which contributesignificant distortion. Field measurements associated with these systemelements are disregarded when performing the position calculation. Insome embodiments, a distortion-contributing element may be deactivated.

There is therefore provided, in accordance with an embodiment of thepresent invention, a method for tracking a position of an object,including:

using a field sensor associated with the object to measure fieldstrengths of magnetic fields generated by two or more field generators,wherein a measurement of at least one of the field strengths is subjectto a distortion;

calculating rotation-invariant location coordinates of the objectresponsively to the measured field strengths; and

determining corrected location coordinates of the object by applying tothe rotation-invariant location coordinates a coordinate correctingfunction so as to adjust a relative contribution of each of the measuredfield strengths to the corrected location coordinates responsively tothe distortion in the measured field strengths.

In some embodiments, the method includes inserting the object into anorgan of a patient, and determining the corrected location coordinatesof the object includes tracking the position of the object inside theorgan.

In an embodiment, the distortion is caused by a field-distorting objectsubjected to at least some of the magnetic fields, wherein the objectcomprises at least one material selected from a group consisting ofmetallic, paramagnetic and ferromagnetic materials.

In a disclosed embodiment, the method includes performing calibrationmeasurements of the magnetic fields at respective known coordinatesrelative to the two or more field generators, and deriving thecoordinate correcting function responsively to the calibrationmeasurements. In another embodiment, the distortion is caused by amovable field-distorting object, and performing the calibrationmeasurements includes performing the measurements at different locationsof the field-distorting object. Additionally or alternatively, derivingthe coordinate correcting function includes applying a fitting processto a dependence of the calibration measurements on the knowncoordinates.

In yet another embodiment, applying the coordinate correcting functionincludes applying a polynomial function having coefficients includingexponents of at least some of the rotation-invariant locationcoordinates.

In still another embodiment, applying the coordinate correcting functionincludes identifying a distortion-contributing element responsively tothe measured field strengths, and producing the coordinate correctingfunction so as to disregard the measured field strengths that areassociated with the distortion-contributing element.

In some embodiments, the field sensor includes one or more field sensingelements, and identifying the distortion-contributing element includesdetermining that one or more of the field sensing elements and the fieldgenerators are contributing to the distortion.

In an embodiment, the method includes calculating angular orientationcoordinates of the object.

In another embodiment, the field sensor is used within a working volumeassociated with the two or more field generators, and determining thecorrected location coordinates includes:

dividing the working volume into two or more clusters;

defining for each of the two or more clusters respective two or morecluster coordinate correcting functions; and

applying to each of the rotation-invariant location coordinates one ofthe cluster coordinate correcting functions responsively to a cluster inwhich the rotation-invariant location coordinate falls.

Applying the cluster coordinate correcting functions may includeapplying a weighting function so as to smoothen a transition betweenneighboring clusters.

In yet another embodiment, the method includes measuring the fieldstrengths using two or more field sensors having non-concentriclocations, and compensating for inaccuracies caused by thenon-concentric locations in the corrected location coordinates.

There is additionally provided, in accordance with an embodiment of thepresent invention, a method for tracking a position of an object,including:

using a field sensor associated with the object to perform measurementsof field strengths of magnetic fields generated by two or more fieldgenerators so as to provide redundant location information, wherein atleast some of the field strength measurements are subject to adistortion; and

determining location coordinates of the object relative to the two ormore field generators by applying to the measurements a coordinatecorrecting function that exploits the redundant location information soas to reduce an impact of the distortion on the location coordinates.

There is also provided, in accordance with an embodiment of the presentinvention, a method for tracking a position of an object, including:

using a field sensor, which includes one or more field sensing elementsassociated with the object, to measure field strengths of magneticfields generated by two or more field generators, wherein a measurementof at least one of the field strengths is subject to a distortion;

identifying, responsively to the measured field strengths, at least onedistortion-contributing system element, which is selected from a groupconsisting of the one or more field sensing elements and the two or morefield generators; and

determining the position of the object relative to the two or more fieldgenerators responsively to the measured field strengths whiledisregarding field measurements associated with thedistortion-contributing system element.

In an embodiment, the method includes inserting the object into an organof a patient, and determining the position of the object includestracking the position of the object inside the organ. In anotherembodiment, the two or more field generators are associated with theobject, and the field sensor is located externally to the organ. In yetanother embodiment, identifying the distortion-contributing systemelement includes accepting an a-priori indication selected from a groupconsisting of a characteristic direction of the distortion and anidentity of the distortion-contributing system element.

In still another embodiment, identifying the distortion-contributingsystem element includes sensing a presence of the distortion in thefield measurements associated with the distortion-contributing systemelement. In an embodiment, the distortion-contributing system elementincludes a pair of one of the field sensing elements and one of thefield generators. In another embodiment, disregarding the fieldmeasurements associated with the distortion-contributing system elementincludes deactivating the distortion-contributing system element.

There is further provide, in accordance with an embodiment of thepresent invention, a system for tracking a position of an object,including:

two or more field generators, which are arranged to generate respectivemagnetic fields in a vicinity of the object;

a field sensor associated with the object, which is arranged to measurefield strengths of the magnetic fields, wherein a measurement of atleast one of the field strengths is subject to a distortion; and

a processor, which is arranged to calculate rotation-invariant locationcoordinates of the object responsively to the measured field strengths,and to determine corrected location coordinates of the object byapplying to the rotation-invariant location coordinates a coordinatecorrecting function so as to adjust a relative contribution of each ofthe measured field strengths to the corrected location coordinatesresponsively to the distortion in the measured field strengths.

There is additionally provided, in accordance with an embodiment of thepresent invention, a system for tracking a position of an object,including:

two or more field generators, which are arranged to generate respectivemagnetic fields in a vicinity of the object;

a field sensor associated with the object, which is arranged to performmeasurements of field strengths of the magnetic fields so as to provideredundant location information, wherein at least some of the fieldstrength measurements are subject to a distortion; and

a processor, which is arranged to determine location coordinates of theobject relative to the two or more field generators by applying to themeasurements a coordinate correcting function that exploits theredundant location information so as to reduce an impact of thedistortion on the location coordinates.

There is also provided, in accordance with an embodiment of the presentinvention, a system for tracking a position of an object, including:

two or more field generators, which are arranged to generate respectivemagnetic fields in a vicinity of the object;

a field sensor, which is associated with the object and includes one ormore field sensing elements, which is arranged to measure fieldstrengths of the magnetic fields, wherein a measurement of at least oneof the field strengths is subject to a distortion; and

a processor, which is arranged to identify responsively to the measuredfield strengths a distortion-contributing system element, which isselected from a group consisting of the one or more field sensingelements and the two or more field generators, and to determine theposition of the object relative to the two or more field generatorswhile disregarding field measurements associated with thedistortion-contributing system element.

There is further provided, in accordance with an embodiment of thepresent invention, a computer software product used in a system fortracking a position of an object, the product including acomputer-readable medium, in which program instructions are stored,which instructions, when read by the computer, cause the computer tocontrol two or more field generators so as to generate magnetic fieldsin a vicinity of the object, to accept measurements of field strengthsof the magnetic fields performed by a field sensor associated with theobject, wherein a measurement of at least one of the field strengths issubject to a distortion, to calculate rotation-invariant locationcoordinates of the object responsively to the measured field strengths,and to determine corrected location coordinates of the object byapplying to the rotation-invariant location coordinates a coordinatecorrecting function so as to adjust a relative contribution of each ofthe measured field strengths to the corrected location coordinatesresponsively to the distortion in the measured field strengths.

There is also provided, in accordance with an embodiment of the presentinvention, a computer software product used in a system for tracking aposition of an object, the product including a computer-readable medium,in which program instructions are stored, which instructions, when readby the computer, cause the computer to control two or more fieldgenerators so as to generate magnetic fields in a vicinity of theobject, to accept measurements of field strengths of the magnetic fieldsperformed by a field sensor associated with the object, the measurementsincluding redundant location information, wherein at least some of themeasurements are subject to a distortion, and to determine locationcoordinates of the object relative to the two or more field generatorsby applying to the measurements a coordinate correcting function thatexploits the redundant location information so as to reduce an impact ofthe distortion on the location coordinates.

There is additionally provided, in accordance with an embodiment of thepresent invention, a computer software product used in a system fortracking a position of an object, the product including acomputer-readable medium, in which program instructions are stored,which instructions, when read by the computer, cause the computer tocontrol two or more field generators so as to generate magnetic fieldsin a vicinity of the object, to accept measurements of field strengthsof the magnetic fields performed by a field sensor, which is associatedwith the object and includes one or more field sensing elements, whereina measurement of at least one of the field strengths is subject to adistortion, to identify responsively to the measured field strengths adistortion-contributing system element, which is selected from a groupconsisting of the two or more field generators and the one or more fieldsensing elements, and to determine the position of the object relativeto the two or more field generators while disregarding fieldmeasurements associated with the distortion-contributing system element.

The present invention will be more fully understood from the followingdetailed description of the embodiments thereof, taken together with thedrawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic, pictorial illustration of a system for positiontracking and steering of intrabody objects, in accordance with anembodiment of the present invention;

FIG. 2 is a schematic, pictorial illustration of a location pad, inaccordance with an embodiment of the present invention;

FIG. 3 is a schematic, pictorial illustration of a catheter, inaccordance with an embodiment of the present invention;

FIG. 4 is a flow chart that schematically illustrates a method forposition tracking in the presence of field distortion, in accordancewith an embodiment of the present invention; and

FIG. 5 is a flow chart that schematically illustrates a method forposition tracking in the presence of field distortion, in accordancewith another embodiment of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS System Description

FIG. 1 is a schematic, pictorial illustration of a system 20 forposition tracking and steering of intrabody objects, in accordance withan embodiment of the present invention. System 20 tracks and steers anintrabody object, such as a cardiac catheter 24, which is inserted intoan organ, such as a heart 28 of a patient. System 20 also measures,tracks and displays the position (i.e., the location and orientation) ofcatheter 24. In some embodiments, the catheter position is registeredwith a three-dimensional model of the heart or parts thereof. Thecatheter position with respect to the heart is displayed to a physicianon a display 30. The physician uses an operator console 31 to steer thecatheter and to view its position during the medical procedure.

System 20 can be used for performing a variety of intra-cardiac surgicaland diagnostic procedures in which navigation and steering of thecatheter is performed automatically or semi-automatically by the system,and not manually by the physician. The catheter steering functions ofsystem 20 can be implemented, for example, by using the Niobe® magneticnavigation system produced by Stereotaxis, Inc. (St. Louis, Mo.).Details regarding this system are available at www.stereotaxis.com.Methods for magnetic catheter navigation are also described, forexample, in U.S. Pat. Nos. 5,654,864 and 6,755,816, whose disclosuresare incorporated herein by reference.

System 20 positions, orients and steers catheter 24 by applying amagnetic field, referred to herein as a steering field, in a workingvolume that includes the catheter. An internal magnet is fitted into thedistal tip of catheter 24. (Catheter 24 is shown in detail in FIG. 3below.) The steering field steers (i.e., rotates and moves) the internalmagnet, thus steering the distal tip of catheter 24.

The steering field is generated by a pair of external magnets 36,typically positioned on either side of the patient. In some embodiments,magnets 36 comprise electro-magnets that generate the steering fieldresponsively to suitable steering control signals generated by console31. In some embodiments, the steering field is rotated or otherwisecontrolled by physically moving (e.g., rotating) external magnets 36 orparts thereof. The difficulties that arise from having large metallicobjects whose position may very over time, such as magnets 36, in closeproximity to the working volume will be discussed hereinbelow.

System 20 measures and tracks the location and orientation of catheter24 during the medical procedure. For this purpose, the system comprisesa location pad 40.

FIG. 2 is a schematic, pictorial illustration of location pad 40, inaccordance with an embodiment of the present invention. Location pad 40comprises field generators, such as field generating coils 44. Coils 44are positioned at fixed, known locations and orientations in thevicinity of the working volume. In the exemplary configuration of FIGS.1 and 2, location pad 40 is placed horizontally under the bed on whichthe patient lies. Pad 40 in this example has a triangular shape andcomprises three tri-coils 42. Each tri-coil 42 comprises three fieldgenerating coils 44. Thus, in the present example, location pad 40comprises a total of nine field generating coils. The three coils 44 ineach tri-coil 42 are oriented in mutually-orthogonal planes. Inalternative embodiments, location pad 40 may comprise any number offield generators arranged in any suitable geometrical configuration.

Referring to FIG. 1, console 31 comprises a signal generator 46, whichgenerates drive signals that drive coils 44. In the embodiments shown inFIGS. 1 and 2, nine drive signals are generated. Each coil 44 generatesa magnetic field, referred to herein as a tracking field, responsivelyto the respective drive signal driving it. The tracking fields comprisealternating current (AC) fields. Typically, the frequencies of the drivesignals generated by signal generator 46 (and consequently thefrequencies of the respective tracking fields) are in the range ofseveral hundred Hz to several KHz, although other frequency ranges canbe used as well.

A position sensor fitted into the distal tip of catheter 24 senses thetracking fields generated by coils and produces respective positionsignals, which are indicative of the location and orientation of thesensor with respect to the field generating coils. The position signalsare sent to console 31, typically along a cable running through catheter24 to the console. Console 31 comprises a tracking processor 48, whichcalculates the location and orientation of catheter 24 responsively tothe position signals. Processor 48 displays the location and orientationof the catheter, typically expressed as a six-dimensional coordinate, tothe physician using display 30.

Processor 48 also controls and manages the operation of signal generator46. In some embodiments, field generating coils 44 are driven by drivesignals having different frequencies, so as to differentiate betweentheir magnetic fields. Alternatively, the field generating coils can bedriven sequentially so that the position sensor measures the trackingfield originating from a single coil 44 at any given time. In theseembodiments, processor 48 alternates the operation of each coil 44 andassociates the position signals received from the catheter with theappropriate field generating coil.

Typically, tracking processor 48 is implemented using a general-purposecomputer, which is programmed in software to carry out the functionsdescribed herein. The software may be downloaded to the computer inelectronic form, over a network, for example, or it may alternatively besupplied to the computer on tangible media, such as CD-ROM. The trackingprocessor may be integrated with other computing functions of console31.

FIG. 3 is a schematic, pictorial illustration of the distal tip ofcatheter 24, in accordance with an embodiment of the present invention.Catheter 24 comprises an internal magnet 32 and a position sensor 52, asdescribed above. Catheter 24 may also comprise one or more electrodes56, such as ablation electrodes and electrodes for sensing localelectrical potentials. Position sensor 52 comprises field sensingelements, such as field sensing coils 60. In some embodiments, positionsensor 52 comprises three field sensing coils 60 oriented in threemutually-orthogonal planes. Each coil 60 senses one of the threeorthogonal components of the AC tracking field and produces a respectiveposition signal responsively to the sensed component. Sensor 52 andelectrodes 56 are typically connected to console 31 via cables 64running through the catheter.

It is well known in the art that metallic, paramagnetic andferromagnetic objects (collectively referred to herein asfield-distorting objects) placed in an AC magnetic field causedistortion of the field in their vicinity. For example, when a metallicobject is subjected to an AC magnetic field, eddy currents are inducedin the object, which in turn produce parasitic magnetic fields thatdistort the AC magnetic field. Ferromagnetic objects distort themagnetic field by attracting and changing the density and orientation ofthe field lines.

In the context of a magnetic position tracking system, when afield-distorting object is present in the vicinity of position sensor52, the tracking field sensed by sensor 52 is distorted, causingerroneous position measurements. The severity of the distortiongenerally depends on the amount of field-distorting material present, toits proximity to the position sensor and to the field generating coils,and/or to the angle in which the tracking field impinges on thefield-distorting object. In the system of FIG. 1, for example, externalmagnets 36 typically contain a large mass of field-distorting materialand are located in close proximity to the working volume. As such,external magnets 36 may cause a significant distortion of the trackingfield sensed by the position sensor.

The methods and systems described hereinbelow are mainly concerned withperforming accurate position tracking measurements in the presence ofsevere distortion of the tracking magnetic field. The catheter steeringsystem of FIG. 1 is described purely as an exemplary application, inwhich objects located in or near the working volume of the positiontracking system cause a severe, time varying distortion of the trackingfield. However, embodiments of the present invention are in no waylimited to magnetic steering applications. The methods and systemsdescribed herein can be used in any other suitable position trackingapplication for reducing such distortion effects. For example, themethods and systems described herein can be used to reduce fielddistortion effects caused by object such as C-arm fluoroscopes andmagnetic resonance imaging (MRI) equipment.

In alternative embodiments, system 20 can be used to track various typesof intrabody objects, such as catheters, endoscopes and orthopedicimplants, as well as for tracking position sensors coupled to medicaland surgical tools and instruments.

Distortion Reduction Method Using Redundant Measurement Information

As noted above, system 20 comprises nine field generating coils 44 thatgenerate nine respective tracking fields. Each of these fields is sensedby three field sensing coils 60. Thus, the system performs a total of 27field projection measurements in order to calculate the six location andorientation coordinates of catheter 24. It is evident that the 27measurements contain a significant amount of redundant information. Thisredundant information can be used to improve the immunity of the systemto distortions caused by field-distorting objects, such as externalmagnets 36.

The 27 field measurements can be viewed as vectors in a 27-dimensionalvector space. Each dimension of this vector space corresponds to a pairof {field generating coil 44, field sensing coil 60}. Because of theredundancy in the measurements, it is often possible to determine alower dimensionality sub-space of this vector space that is invariant ornearly invariant to the field distortions. The position tracking methoddescribed in FIG. 4 below uses the redundant information present in thefield measurements to improve the accuracy of the position measurementsin the presence of such field distortions.

In principle, the method first calculates three location vectors thatdefine the location of position sensor 52 relative to the threetri-coils 42, respectively. These location vectors are invariant to theangular orientation of the position sensor and are referred to asrotation invariants. The location vectors are orientation-invariantsince, as will be shown below, they are calculated based on measuredfield intensity and not based on the projection of the field strengthonto the field sensing coils.

The location vectors (rotation invariants) are corrected by coordinatecorrecting functions, which exploit the redundant measurementinformation to improve field distortion immunity. The orientationcoordinates of the position sensor are then calculated to complete thesix-dimensional location and orientation coordinate of the sensor. Insome embodiments, the method of FIG. 4 also comprises calibration andclustering steps, as well as a process for compensating for thenon-concentricity of coils 60 of position sensor 52.

Although the method of FIG. 4 below refers to a location pad comprisingnine field generating coils arranged in three mutually-orthogonal groupsin tri-coils 42 and to a position sensor comprising threemutually-orthogonal field sensing coils, this configuration is anexemplary configuration chosen purely for the sake of conceptualclarity. In alternative embodiments, location pad 40 and position sensor52 may comprise any number of coils 44 and coils 60 arranged in anysuitable geometrical configuration.

FIG. 4 is a flow chart that schematically illustrates a method forposition tracking in the presence of field distortion, in accordancewith an embodiment of the present invention. The method begins bymapping and calibrating the tracking fields generated by location pad40, at a calibration step 100.

Typically, the calibration process of step 100 is performed during theproduction of location pad 40, and the calibration results are stored ina suitable memory device coupled to the location pad. Calibration setupsthat can be used for this purpose and some associated calibrationprocedures are described, for example, in U.S. Pat. No. 6,335,617, whosedisclosure is incorporated herein by reference.

In the calibration process, a calibrating sensor similar to positionsensor 52 is scanned through multiple locations in the three-dimensionalworking volume around pad 40. At each location of the calibratingsensor, each of the nine field generating coils 44 in pad 40 is drivento generate a respective tracking field, and the three field sensingcoils 60 of the calibrating sensor measure this tracking field. Thesensed field strengths associated with each location are recorded.

In some embodiments, the calibration process comprises performingmultiple field measurements at each location of the calibrating sensor.Typically, some of these measurements comprise free-space measurements(i.e., measurements taken when the working volume and its vicinity arefree of field-distorting objects). Other measurements are taken in thepresence of field-distorting objects, in the same positions they areexpected to have during the system operation. For example, when thefield-distorting objects comprise external magnets 36 that arephysically moved to steer catheter 24, field measurements are performedwhile the magnets are moved through their entire expected motion range.Other field-distorting objects that may be included in the calibrationinclude, for example, a fluoroscope used to irradiate the patient, aswell as the bed the patient lies on.

The calibration setup performs the field measurements and records themeasurement results along with the associated known locations of thecalibrating sensor. In some embodiments, the calibration procedure iscarried out by a robot or other automatic calibration setup that movesthe calibration sensor across the working volume around pad 40.

In some embodiments, every pad 40 being produced is calibrated using thecalibration procedure described herein. Alternatively, such as when theproduction process of pads 40 is sufficiently repeatable, the fullcalibration procedure may be performed only on a single location pad ora sample of pads and the results used to calibrate the remaining pads.Further alternatively, a sample of pads may be subjected to the fullcalibration procedure. For the remaining pads, only differentialresults, indicating the field strength differences between free-spacemeasurements and distorted measurements, are recorded.

In some cases, the material composition, mechanical structure and/orlocation of the field-distorting objects is known. In such cases, theinterference caused by these objects can be modeled, and the model usedas part of the calibration measurements. In some cases, when multiplefield-distorting objects are present, calibration measurements may beperformed for each object separately. The individual calibrationmeasurements can then be combined. Further additionally oralternatively, any other suitable method of obtaining a set ofcalibration measurements can be used.

The multiple field projection measurements, each associated with a knownlocation of the calibrating sensor, are used to derive threerotation-invariant coordinate correcting functions. The correctingfunctions will later be applied during normal system operation. Thefunctions accept as input a set of raw field measurements, as measuredby position sensor 52. These raw measurements may be distorted due tothe presence of field-distorting objects. The three functions producethree respective corrected location coordinates of position sensor 52with respect to location pad 40. In some embodiments, the correctingfunctions compensate for distortion from field-distorting objects, aswell as for errors due to the fact that the tracking fields generated bycoils 44 deviate from ideal dipole fields. Modeling the tracking fieldsas dipole fields is, however, not mandatory.

In some embodiments, the coordinate correcting functions are determinedusing a fitting process. The fitting process determines the functionsthat best fit the location coordinates measured during calibration step100 above to the known location coordinates of the calibrating sensor.Any suitable fitting method known in the art can be used for thispurpose, such as, for example, polynomial regression methods.

Thus, the fitting process effectively causes the coordinate correctingfunctions to adjust the relative contribution of each raw locationcoordinate to the corrected location coordinate responsively to thelevel of distortion contained in the raw measurements. Raw locationcoordinates having low distortion content are likely to be emphasized,or given more weight, by the fitting process. Raw location coordinateshaving high distortion content are likely to be given less weight, oreven ignored.

The coordinate correcting functions can thus be viewed as transformingthe raw field measurements into a sub-space that is as invariant aspossible to the distortion. Since the fitting process takes intoconsideration the bulk of calibration measurements, the sub-space isinvariant to the distortion caused in different field-distorting objectgeometries.

In some embodiments, the coordinate correcting function can disregardfield measurements associated with one or more distortion-contributingsystem elements that contribute a significant amount of distortion tothe calculation. Distortion-contributing elements may comprise fieldgenerating coils 44, field sensing coils and/or pairs of {coil 44, coil60}. In these embodiments, the function may ignore the measurementsrelated to the distortion-contributing elements, for example by settingappropriate coefficients of the coordinate correcting function to zeroor otherwise shaping the function to be insensitive to these elements.In some embodiments, the distortion-contributing elements can beswitched off or otherwise deactivated.

The raw location coordinates are expressed as three vectors denotedr_(tc), wherein tc=1 . . . 3 indicates an index of the tri-coil 42 usedin the measurement. Vector r_(tc) comprises three location coordinates{x_(tc),y_(tc),z_(tc)} indicating the location coordinates of theposition sensor, as calculated responsively to the tracking fieldsgenerated by tri-coil tc. By convention, r_(tc) is expressed relative toa reference frame of location pad 40. An exemplary mathematicalprocedure for calculating r_(tc) based on the measured field strengths,assuming an ideal dipole field, is given in step 102 further below.

In some embodiments, the three coordinate correcting functions comprisepolynomial functions. In the description that follows, each functioncomprises a third-order polynomial of the location coordinates that doesnot contain any cross-terms (i.e., the polynomial may contain x, x², x³,y, y², y³, z, z² and z³ terms but not, for example, xy², xyz or y²zterms). The input to the coordinate correcting functions can thus beexpressed as a 28-dimensional vector denoted In, which is defined asIn={1, r₁, r₂, r₃, r₁ ², r₂ ², r₃ ², r₁ ³, r₂ ³, r₃ ³}={1, x₁, y₁, z₁,x₂, y₂, z₂, x₃, y₃, z₃, x₁ ², y₁ ², z₁ ², x₂ ², y₂ ², z₂ ², x₃ ², y₃ ²,z₃ ², x₁ ³, y₁ ³, z₁ ³, x₂ ³, y₂ ³, z₂ ³, x₃ ³, y₃ ³, z₃ ³}, wherein thefirst “1” term serves as an offset. The three coordinate correctingfunctions have the form

$\begin{matrix}{{x_{cor} = {\sum\limits_{i = 1}^{28}{\alpha_{i}{In}_{i}}}}{y_{cor} = {\sum\limits_{i = 1}^{28}{\beta_{i}{In}_{i}}}}{z_{cor} = {\sum\limits_{i = 1}^{28}{\gamma_{i}{In}_{i}}}}} & \lbrack 1\rbrack\end{matrix}$

wherein x_(cor), y_(cor) and z_(cor) respectively denote thedistortion-corrected x, y and z location coordinates of position sensor52, with respect to location pad 40. Coefficients α₁ . . . α₂₈, β₁ . . .β₂₈ and γ₁ . . . γ₂₈ denote the coefficients of the polynomialfunctions. In the present example, The fitting process described abovecomprises fitting the values of the polynomial coefficients.

The three sets of coefficients can be arranged in a coefficient matrixdenoted L_(coeff), defined as

$\begin{matrix}{L_{coeff} = \begin{bmatrix}\alpha_{1} & \beta_{1} & \gamma_{1} \\\alpha_{2} & \beta_{2} & \gamma_{2} \\\ldots & \ldots & \ldots \\\alpha_{28} & \beta_{28} & \gamma_{28}\end{bmatrix}} & \lbrack 2\rbrack\end{matrix}$

Using this representation, the corrected location coordinates of theposition sensor are given by

r _(cor) ={x _(cor) ,y _(cor) ,z _(cor) }=In·L _(coeff)  [3]

In order to further clarify the effectiveness of the coordinatecorrecting functions, consider a particular location of the calibrationsensor. During the calibration process of step 100, multiple fieldstrength measurements are performed at this particular location, both infree space and in the presence of distortion from differentfield-distorting objects, as expected to occur during the normaloperation of the system. The coordinate correcting functions replacethese multiple measurements with a single corrected value, which bestfits the known location coordinate of the calibrating sensor.

The coordinate correcting functions effectively exploit the redundantinformation contained in the 27 raw location measurements to improvedistortion immunity. For example, since the intensity of a magneticfield decays rapidly with distance (proportionally to 1/r³),measurements performed using a tri-coil 42 that is further away from thefield-distorting object will typically produce measurements containingless distortion. In such cases, the fitting process will typically givea higher weight to the measurements associated with this lowerdistortion tri-coil when calculating coefficients ∝_(i), β_(i) and γ_(i)of the coordinate correcting functions.

As another example, in many cases, the field distortion is highlysensitive to the angle in which of the magnetic field impinges on thefield-distorting object. Since the three field generating coils 44 ineach tri-coil 42 are mutually-orthogonal, there will typically exist atleast one coil 44 whose tracking field generates little or nodistortion. Again, the fitting process used to calculate coefficients∝_(i), β_(i) and γ_(i) will typically give a higher weight to themeasurements associated with this lower distortion coil 44.

In summary, calibration step 100 comprises mapping the working volumearound location pad 40, followed by derivation of coordinate correctingfunctions that will later on translate measured raw location coordinatesto distortion-corrected location coordinates of position sensor 52.

Steps 102-110 below are carried out by tracking processor 48 during thenormal operation of system 20, whenever a position tracking measurementis desired. Processor 48 calculates the rotation-invariant locationcoordinates r_(tc) (also referred to as the raw location coordinates),at an invariant calculation step 102. As noted above, the calculationthat follows assumes that the tracking fields generated by coils 44 areideal dipole fields.

For each tri-coil 42 having an index tc=1 . . . 3, processor 48calculates a field intensity matrix denoted MtM, which is defined as

MtM=(U _(tc) ·M _(tc))^(t)·(U _(tc) ·M _(tc))  [4]

wherein U_(tc) is a 3-by-3 matrix containing the field strengths of thetracking fields generated by the three field generating coils 44 oftri-coil tc, as measured by the three field sensing coils 60 of positionsensor 52. Each matrix element (U_(tc))_(ij) denotes the field strengthgenerated by the j^(th) field generating coil 44 in tri-coil tc, assensed by the i^(th) field sensing coil 60 of sensor 52. Matrix M_(tc),is a 3-by-3 matrix comprising the inverse of the magnetic moment matrixof tri-coil tc. The operator ( )^(t) denotes matrix transposition.

Processor 48 now calculates ∥r∥, which denotes the radius-vector, ormagnitude, of location vector r_(tc). ∥r∥ is given by∥r∥=Trace(⁶√{square root over (MtM/6)}).

The direction of vector r_(tc) is approximated by the direction of theeigenvector of matrix MtM corresponding to the largest eigenvalue. Inorder to determine this eigenvector, processor 48 applies a singularvalue decomposition (SVD) process, as is known in the art, to matrixMtM:

[u,w,u ^(t)]=SVD(MtM)  [5]

wherein u denotes the eigenvectors and w denotes the eigenvalues ofmatrix MtM.

Let u(1) denote the eigenvector corresponding to the largest eigenvalue.In order to resolve ambiguity, the z-axis component of u(1) (byconvention, the third component of the eigenvector) is forced to bepositive by selecting the mirror image of the vector u(1) if necessary.In other words, IF u(1).{0,0,1}<0 THEN u(1)=−u(1). Finally, the rawlocation coordinate vector r_(tc) is estimated by

r _(tc) =∥r∥·u(1)+c _(tc)  [6]

wherein c_(tc) denotes the location coordinate vector of tri-coil tc inthe coordinate system of location pad 40.

Tracking processor 48 typically repeats the process of step 102 for allthree tri-coils 42 of pad 40. The output of step 102 is three vectorsr_(tc), tc=1 . . . 3, giving the raw location coordinates of positionsensor 52 relative to tri-coils 42. As noted above, the raw locationcoordinates are uncorrected and may contain distortion caused byfield-distorting objects.

Processor 48 now calculates the distortion-corrected locationcoordinates of sensor 52, at a corrected coordinate calculation step104. Processor 48 uses the coordinate correcting functions calculated atcalibration step 100 above for this purpose. In the exemplary embodimentdescribed above, in which the functions comprise third-orderpolynomials, the three coordinate correcting functions are expressed interms of matrix L_(coeff), as defined in equation [2] above. In thisembodiment, vector r_(cor) denoting the distortion-corrected locationcoordinates of sensor 52 is given by

r _(cor) =In·L _(coeff)  [7]

wherein In denotes the input vector of raw location coordinates andtheir exponents, as described above. In alternative embodiments, vectorr_(cor) is calculated by applying the coordinate correction functions tothe measured raw location coordinates.

In some embodiments, tracking processor 48 applies a clustering processto the location measurements, at a clustering step 106. The accuracy ofthe coordinate correcting functions can often be improved by dividingthe working volume into two or more sub-volumes, referred to asclusters, and defining different coordinate correcting functions foreach cluster.

Let N denote the number of clusters. In embodiments in which thecoordinate correcting functions are expressed in terms of matrixL_(coeff), for example, processor 48 calculates for each cluster c (c=1. . . N) a cluster coefficient matrix denoted L_(coeff-c) at calibrationstep 100 above. At step 104 above, processor 48 determines the clusterto which each raw location coordinate measurement belongs, and appliesthe appropriate cluster coefficient matrix to produce thedistortion-corrected location coordinates.

In some embodiments, the transitions between neighboring clusters aresmoothed using a weighting function. In these embodiments, a prototypecoordinate denoted p_(c) is defined for each cluster c, typicallylocated in the center of the cluster. Processor 48 calculates a weightedcorrected coordinate denoted r_(w) by summing the corrected locationcoordinates calculated using the coordinate correcting functions of eachcluster, weighted by the distance of the raw coordinate r from theprototype coordinate p_(c) of the cluster:

$\begin{matrix}{r_{w} = {\sum\limits_{i = 1}^{N}{{f\left( {r - p_{c}} \right)} \cdot {In} \cdot L_{{coeff} - c}}}} & \lbrack 8\rbrack\end{matrix}$

The weighting function f(r−p_(c)) is defined as

$\begin{matrix}{{f\left( {r - p_{c}} \right)} = \frac{1}{1 + \left( \frac{r - p_{c}}{a} \right)^{2\; t}}} & \lbrack 9\rbrack\end{matrix}$

wherein a and t are constants used to appropriately shape the weightingfunction.

In some embodiments, processor 48 verifies that the raw locationcoordinate being processed is indeed located inside the working volumemapped at step 100 above. This validity check is sometimes desirable inorder to ensure that the coordinate correcting functions being used areindeed valid for the coordinate in question. In some embodiments, if theraw location coordinate is found to be outside the mapped workingvolume, processor 48 notifies the physician of the situation, such as bydisplaying the coordinate using a different color or icon or bypresenting an alert message. In some embodiments, the raw coordinate isdisplayed without applying correction. Alternatively, the measurementmay be discarded.

For example, in some embodiments, processor 48 produces a validitymatrix denoted V during calibration step 100. Matrix V comprises athree-dimensional bit matrix, in which each bit corresponds to athree-dimensional voxel (i.e., a unit volume, the three-dimensionalequivalent of a pixel) in the working volume having a resolution denotedd. Each bit of matrix V is set if the corresponding voxel coordinate iswithin the mapped working volume, otherwise the bit is reset.

In order to preserve memory space, matrix V can be represented as atwo-dimensional array of 32-bit words. The two indices of the arraycorrespond to the x and y coordinates of the voxel, and each bit in theindexed 32-bit word corresponds to the z-axis coordinate of the voxel.The following pseudo-code shows an exemplary method for indexing matrixV in order to verify whether a coordinate {x,y,z} is located within thevalid working volume:

{xInx,yInx,zInx}=round[({x,y,z}−{x ₀ ,y ₀ ,z ₀})/d];

xInx=Max[MinX,Min[MaxX,xInx];

yInx=Max[MinY,Min[MaxY,xIny];

zInx=Max[MinZ,Min[MaxZ,xInz];

valid=bitSet[V(xInx,yInx),zInx];

wherein round[x] denotes the integer closest to x, and {x₀,y₀,z₀} denotethe corner coordinates of the mapped working volume. {xInx,yInx,zInx}denote indices to matrix V. MinX, MaxX, MinY, MaxY, MinZ, MaxZ denoterange limits of the x, y and z coordinates, respectively. If theextracted valid bit is set, processor 48 concludes that coordinate{x,y,z} is located within the mapped working volume, and vice versa.

In some embodiments, two or more validity matrices may be defined. Forexample, the boundary, or outskirts, of the working volume may be mappedseparately and defined using a second validity matrix.

At this stage, processor 48 has calculated a distortion-correctedlocation coordinate of position sensor 52, typically expressed as athree-dimensional coordinate. In order to obtain the completesix-dimensional coordinate of the position sensor, processor 48 nowcalculates the angular orientation coordinates of the position sensor,at an orientation calculation step 108.

In some embodiments, the orientation coordinates are calculated usingthe relation

M _(tc) =R·B _(tc)

wherein M_(tc), denotes the inverse moment matrix described above, Rdenotes a rotation matrix representing the angular orientation of sensor52 with respect to the coordinate system of location pad 40, and B_(tc)denotes the measured magnetic field at coils 60 of sensor 52.

Matrix R can be estimated by

R=M·B ^(t)·(B·B ^(t))⁻¹  [10]

wherein

$M = {{\begin{bmatrix}M_{1} \\M_{2} \\M_{3}\end{bmatrix}\mspace{14mu} {and}\mspace{14mu} b} = {\begin{bmatrix}B_{1} \\B_{2} \\B_{3}\end{bmatrix}.}}$

The measurements of B_(tc) may contain distortion from field-distortingobjects, which may in turn affect the estimation accuracy of matrix R.The estimation accuracy may be improved by applying a symmetricaldecomposition process to R. For example, let R²=R^(t)·R. Processor 48applies a SVD process to R²:

$\begin{matrix}{{V \cdot \begin{bmatrix}u_{1}^{2} & 0 & 0 \\0 & u_{2}^{2} & 0 \\0 & 0 & u_{3}^{2}\end{bmatrix} \cdot V^{t}} = {{SVD}\left\lbrack R^{2} \right\rbrack}} & \lbrack 11\rbrack\end{matrix}$

wherein u₁ ², u₂ ² and u₃ ² denote the eigenvalues of R². Define S as:

$\begin{matrix}{S = \left( {{- R^{2}} + {\left( {{u_{1} \cdot \left( {u_{1} + u_{2}} \right)} + {u_{2} \cdot \left( {u_{2} + u_{3}} \right)} + {u_{3} \cdot \left( {u_{3} + u_{1}} \right)}} \right) \cdot R^{2}} + {u_{1} \cdot u_{2} \cdot u_{3} \cdot {\left( {u_{1} + u_{2} + u_{3}} \right)\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{bmatrix}}}} \right.} & \lbrack 12\rbrack\end{matrix}$

Processor 48 calculates an improved accuracy rotation matrix denoted{tilde over (R)}, which is given by:

{tilde over (R)}=R·S ⁻¹  [13]

Having calculated the distortion-corrected location and orientationcoordinates, processor 48 now has the full six-dimensional coordinatesof position sensor 52.

Until now it was assumed that field sensing coils 60 of position sensor52 are concentric, i.e., have identical location coordinates. In somecases, however, sensor 52 is constructed so that coils 60 are notconcentric. This non-concentricity introduces an additional inaccuracyinto the distortion-corrected coordinates. In some embodiments, trackingprocessor 48 compensates for the inaccuracies caused by thenon-concentricity of the field sensing coils, at a non-concentricitycompensation step 110.

For example, processor 48 may apply an iterative compensation process tocompensate for such inaccuracies. Consider the tracking field denotedME_(tc,co), which is generated by a coil co of tri-coil tc and measuredby a non-concentric position sensor 52. Let vector {right arrow over(r)} denote the location coordinate of one of coils 60 of the sensor,used as a reference coordinate, with respect to tri-coil tc. Let {rightarrow over (r)}c₁ and {right arrow over (r)}_(c2) denote two vectorsdefining the location offsets of the other two field sensing coils withrespect to the first (reference) coil. The tracking field generated bycoil co of tri-coil tc in sensor 52 is given by:

$\begin{matrix}{{ME}_{{tc},{co}} = {\overset{\sim}{R} \cdot \begin{bmatrix}{{B_{{tc},{co}}\left( {\overset{\rightarrow}{r} + {R^{t} \cdot {\overset{\rightarrow}{r}}_{c\; 1}}} \right)}(1)} \\{{B_{{tc},{co}}\left( \overset{\rightarrow}{r} \right)}(2)} \\{{B_{{tc},{co}}\left( {\overset{\rightarrow}{r} + {R^{t} \cdot {\overset{\rightarrow}{r}}_{c\; 2}}} \right)}(3)}\end{bmatrix}}} & \lbrack 14\rbrack\end{matrix}$

wherein the second line of the field vector corresponds to the referencecoil. {tilde over (R)} denotes the improved accuracy rotation matrixdefined by equation [13] above.

Processor 48 improves the estimation of ME_(tc,co) by iterativelyrepeating steps 104-108 above. At each iteration step i+1, the measuredfield is given by

$\begin{matrix}{{ME}_{{tc},{co}}^{i + 1} = {{ME}_{{tc},{co}} + {{\overset{\sim}{R}}^{i} \cdot \begin{bmatrix}{{{B_{{tc},{co}}^{i}\left( {\overset{\rightarrow}{r} + {\left( R^{t} \right)^{i} \cdot {\overset{\rightarrow}{r}}_{c\; 1}}} \right)}(1)} - {{B_{{tc},{co}}^{i}\left( \overset{\rightarrow}{r} \right)}(1)}} \\0 \\{{{B_{{tc},{co}}^{i}\left( {\overset{\rightarrow}{r} + {\left( R^{t} \right)^{i} \cdot {\overset{\rightarrow}{r}}_{c\; 2}}} \right)}(3)} - {{B_{{tc},{co}}^{i}\left( \overset{\rightarrow}{r} \right)}(3)}}\end{bmatrix}}}} & \lbrack 15\rbrack\end{matrix}$

In some embodiments, processor 48 performs a predetermined number ofiteration steps. Alternatively, a convergence threshold th is defined,and the iterative process is repeated until

${\left( {{{B_{{tc},{co}}^{i}\left( {\overset{\rightarrow}{r} + {\left( R^{t} \right)^{i} \cdot {\overset{\rightarrow}{r}}_{c\; 1}}} \right)}(1)} - {{B_{{tc},{co}}^{i}\left( \overset{\rightarrow}{r} \right)}(1)}} \right)^{2} + \left( {{{B_{{tc},{co}}^{i}\left( {\overset{\rightarrow}{r} + {\left( R^{t} \right)^{i} \cdot {\overset{\rightarrow}{r}}_{c\; 2}}} \right)}(3)} - {{B_{{tc},{co}}^{i}\left( \overset{\rightarrow}{r} \right)}(3)}} \right)^{2}} < {th}$

Distortion Reduction Method Using Directional Selection

As noted above, in some cases the distortion introduced into aparticular field strength measurement is highly dependent on the mutuallocation and/or orientation of the field generating coil used, the fieldsensing coil used and the field-distorting object causing thedistortion. Therefore, when redundant field measurements are performedusing multiple field generating coils 44 and field sensing coils 60having different locations and orientations, it is often possible toidentify one or more coil 44 and/or coil 60 that are dominantcontributors of distortion. Discarding the measurements related to thesedistortion-contributing system elements may significantly reduce thetotal amount of distortion in the position calculation.

FIG. 5 is a flow chart that schematically illustrates a method forposition tracking in the presence of field distortion, based onrecognizing and eliminating distortion-contributing elements, inaccordance with another embodiment of the present invention. The methodof FIG. 5 refers to a single position tracking calculation, at a singleposition of catheter 24 in the patient's body. This method can beapplied, of course, at multiple positions distributed throughout theworking volume of a position tracking system.

The method begins with system 20 performing redundant fieldmeasurements, at a measurement step 120. Typically, multiple fieldstrength measurements are taken using different pairs of {fieldgenerating coil 44, field sensing coil 60}. As noted above, theexemplary system configuration of FIGS. 1 and 2 comprises a total of 27coil pairs, resulting in a maximum number of 27 redundant fieldmeasurements.

Tracking processor 48 now identifies one or more distortion-contributingmeasurements out of the redundant field measurements, at anidentification step 122. The distortion-contributing measurements arecharacterized by a high level of distortion. In some embodiments,processor 48 may automatically detect and quantify the level ofdistortion in the redundant field measurements. Any suitable method maybe used for this purpose, such as, for example, methods described inU.S. Pat. No. 6,147,480 cited above. Using the distortion-contributingmeasurements, processor 48 identifies one or moredistortion-contributing system elements, which may comprise fieldgenerating coils 44, field sensing coils 60 and/or pairs of {coil 44,coil 60} that are associated with the distortion-contributingmeasurements.

Additionally or alternatively, the characteristic direction of thedistortion may be indicated to processor a-priori. In some cases, theknown direction of distortion indicates to the processor which of coils44 and/or coils 60 is particularly susceptible to the distortion, and istherefore likely to comprise a distortion-contributing element. Furtheralternatively, the identity of a particular coil 44, coil 60 and/or pair{coil 44, coil 60} that produces (or is likely to produce)distortion-contributing measurements can be indicated to the processora-priori.

Tracking processor 48 calculates the position coordinates of positionsensor 52 (and of catheter 24) while disregarding the measurementsassociated with the distortion-contributing elements, at a positioncalculation step 124. In some embodiments, the measurements associatedwith a distortion-contributing element are ignored or discarded from theposition calculation. Alternatively, a particulardistortion-contributing element can be switched off or otherwisedeactivated.

Processor 48 may use any suitable position tracking method forcalculating the position of sensor 52 (and of catheter 24) inconjunction with the method of FIG. 5, such as the method of FIG. 4hereinabove, as well as methods described in some of the publicationscited above.

In some embodiments, the method shown in FIG. 5 above can be similarlyused in system configurations in which the tracking fields are generatedby catheter 24 and sensed by externally-located position sensors. Inthese embodiments, signal generator 46 produces drive signals that drivethe field generators in catheter 24 to produce the tracking fields. Theexternal position sensors sense the tracking fields. The sensed fieldsare then used, in accordance with the appropriate method, to determine adistortion-free position of catheter 24.

Although the embodiments described herein mainly refer to improving thedistortion immunity of medical position tracking and steering systems,these methods and systems can be used in additional applications, suchas for reducing the distortion caused by the operating room table,fluoroscopy equipment, MRI equipment and/or any other field-distortingobject.

It will thus be appreciated that the embodiments described above arecited by way of example, and that the present invention is not limitedto what has been particularly shown and described hereinabove. Rather,the scope of the present invention includes both combinations andsub-combinations of the various features described hereinabove, as wellas variations and modifications thereof which would occur to personsskilled in the art upon reading the foregoing description and which arenot disclosed in the prior art.

1. A method for tracking a position of an object in a working volume,comprising: using a field sensor associated with the object to measurefield strengths of magnetic fields generated by two or more fieldgenerators, the magnetic fields generated by two or more fieldgenerators defining a working volume, wherein a measurement of at leastone of the field strengths is subject to a distortion; calculatinglocation coordinates of the object responsively to the measured fieldstrengths, the raw location coordinates of the object defining rotationinvariant location coordinates of the object; and determining correctedlocation coordinates of the object by applying to the rotation-invariantlocation coordinates a coordinate correcting function so as to adjust arelative contribution of each of the measured field strengths to thecorrected location coordinates responsively to the distortion in themeasured field strengths according to a plurality of sub-volumes of theworking volume.
 2. The method according to claim 1, and comprisinginserting the object into an organ of a patient, wherein determining thecorrected location coordinates of the object comprises tracking theposition of the object inside the organ.
 3. The method according toclaim 1, wherein the distortion is caused by a field-distorting objectsubjected to at least some of the magnetic fields, wherein the objectcomprises at least one material selected from a group consisting ofmetallic, paramagnetic and ferromagnetic materials.
 4. The methodaccording to claim 1, and comprising performing calibration measurementsof the magnetic fields at respective known coordinates relative to thetwo or more field generators, and deriving the coordinate correctingfunction responsively to the calibration measurements.
 5. The methodaccording to claim 4, wherein the distortion is caused by a movablefield-distorting object, and wherein performing the calibrationmeasurements comprises performing the measurements at differentlocations of the field-distorting object.
 6. The method according toclaim 4, wherein deriving the coordinate correcting function comprisesapplying a fitting process to a dependence of the calibrationmeasurements on the known coordinates.
 7. The method according to claim1, wherein applying the coordinate correcting function comprisesapplying a polynomial function having coefficients comprising exponentsof at least some of the rotation-invariant location coordinates.
 8. Themethod according to claim 1, wherein applying the coordinate correctingfunction comprises identifying a distortion-contributing elementresponsively to the measured field strengths, and producing thecoordinate correcting function so as to disregard the measured fieldstrengths that are associated with the distortion-contributing element.9. The method according to claim 8, wherein the field sensor comprisesone or more field sensing elements, and wherein identifying thedistortion-contributing element comprises determining that one or moreof the field sensing elements and the field generators are contributingto the distortion.
 10. The method according to claim 1, and comprisingcalculating angular orientation coordinates of the object.
 11. Themethod according to claim 1, wherein the field sensor is used within aworking volume associated with the two or more field generators, andwherein determining the corrected location coordinates comprises:dividing the working volume into two or more clusters; defining for eachof the two or more clusters respective two or more cluster coordinatecorrecting functions; and applying to each of the rotation-invariantlocation coordinates one of the cluster coordinate correcting functionsresponsively to a cluster in which the rotation-invariant locationcoordinate falls.
 12. The method according to claim 11, wherein applyingthe cluster coordinate correcting functions comprises applying aweighting function so as to smoothen a transition between neighboringclusters.
 13. The method according to claim 1, and comprising measuringthe field strengths using two or more field sensors havingnon-concentric locations, and compensating for inaccuracies caused bythe non-concentric locations in the corrected location coordinates.14-21. (canceled)
 22. A system for tracking a position of an object in aworking volume, comprising: two or more field generators, which arearranged to generate respective magnetic fields in a vicinity of theobject, the respective magnetic fields generated by two or more fieldgenerators defining a working volume; a field sensor associated with theobject, which is arranged to measure field strengths of the magneticfields, wherein a measurement of at least one of the field strengths issubject to a distortion; and a processor, which is arranged to calculateraw location coordinates of the object responsively to the measuredfield strengths, the raw location coordinates of the object definingrotation invariant location coordinates of the object, and to determinecorrected location coordinates of the object by applying to therotation-invariant location coordinates a coordinate correcting functionso as to adjust a relative contribution of each of the measured fieldstrengths to the corrected location coordinates responsively to thedistortion in the measured field strengths according to a plurality ofsub-volumes of the working volume.
 23. The system according to claim 22,wherein the object is adapted to be inserted into an organ of a patient,and wherein the processor is arranged to track the position of theobject inside the organ.
 24. The system according to claim 22, whereinthe distortion is caused by a field-distorting object subjected to atleast some of the magnetic fields, wherein the object comprises at leastone material selected from a group consisting of metallic, paramagneticand ferromagnetic materials.
 25. The system according to claim 22,wherein the coordinate correcting function is determined by performingcalibration measurements of the magnetic fields at respective knowncoordinates relative to the two or more field generators, and derivingthe coordinate correcting function responsively to the calibrationmeasurements.
 26. The system according to claim 25, wherein thedistortion is caused by a movable field-distorting object, and whereinthe calibration measurements comprise measurements taken at differentlocations of the field-distorting object.
 27. The system according toclaim 25, wherein the processor is arranged to apply a fitting processto a dependence of the calibration measurements on the knowncoordinates, so as to derive the coordinate correcting function.
 28. Thesystem according to claim 22, wherein the coordinate correcting functioncomprises a polynomial function having coefficients comprising exponentsof at least some of the rotation-invariant location coordinates.
 29. Thesystem according to claim 22, wherein the processor is arranged toidentify a distortion-contributing element responsively to the measuredfield strengths, and to produce the coordinate correcting function so asto disregard the measured field strengths that are associated with thedistortion-contributing element.
 30. The system according to claim 29,wherein the field sensor comprises one or more field sensing elements,and wherein the processor is arranged to identify that at least oneelement selected from a group consisting of the field sensing elementsand the field generators is contributing to the distortion, so as toidentify the distortion-contributing system element.
 31. The systemaccording to claim 22, wherein the processor is further arranged tocalculate angular orientation coordinates of the object.
 32. The systemaccording to claim 22, wherein the field sensor is used within a workingvolume associated with the two or more field generators, and wherein theprocessor is arranged to divide the working volume into two or moreclusters, to define for each of the two or more clusters respective twoor more cluster coordinate correcting functions, and to apply to each ofthe rotation-invariant location coordinates one of the clustercoordinate correcting functions responsively to a cluster in which therotation-invariant location coordinate falls.
 33. The system accordingto claim 32, wherein the processor is further arranged to apply aweighting function so as to smoothen a transition between neighboringclusters.
 34. The system according to claim 22, and comprising two ormore field sensors having non-concentric locations, wherein theprocessor is arranged to compensate for inaccuracies caused by thenon-concentric locations in the corrected location coordinates. 35-45.(canceled)